Some problems with the implementation of the Constrained Transport method
 

I am having some issues with implementing Constrained Transport method as it makes my MHD Riemann solver much more unstable (than w/o it) although it is able to retain solenoidal magnetic field. However, it is able to preserve solenoidal magnetic field condition as BRx-BLx/dx=0 and BRy-BLy/dy=0 which is weird as the divergence magnetic field states that BRx-BLx/dx+BRy-BLy/dy=0. I guess this may be why my code is not working as my BRx=BLx and BRy=BLy. Any help is deeply appreciated.